Radiation From Solar System Objects
Transcript of Radiation From Solar System Objects
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Radiation from Solar System
Objects
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Types of observation
Photometry: estimating sizes of unresolvedobjects and scattering properties of theirsurface material
Thermal radiometry: sounding the near-surface temperature distribution
Spectrophotometry: identifying minerals orchemical compounds via theirabsorption/emission features
Radar: estimating surface roughness andcomposition; constructing 3D size/shapemodels of visually unresolved objects
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Observing Geometry
External planet: outsidethe Earths orbit
- example:Mars Internal planet: inside the
Earths orbit
- example:Venus
Elongation: angle S-E-P
Phase angle: angle S-P-E
Earth
Planet
Sun
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Phases Opposition: E = (external planets)
Conjunction: E = 0 (all planets)
Quadrature (external planets): E = /2 and
Max. elongation (internal planets): = /2 and
max arctan 1 r2 1
Emax
arcsin r
Phases of Venus:
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Elongations & Phase Angles
Planet |E|max (deg) max (deg)
Mercury
Venus
Mars
Jupiter
SaturnUranus
Neptune
23
46
180
180
180180
180
180
180
41
11
63
2
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Bond Albedo
Albedo= whiteness
R: specularly reflectedflux
S: scattered flux in all
directions I: solar energy flux
AB R S
Isun cosi
AB= fraction not absorbed; 1-AB=absorbed fraction
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Phase Function
Ratio between the fluxscattered at phase angle and the backscattered fluxwith =0
Phase integral:
f() F() /F(0)
q 2 f()sind0
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Geometric Albedo
Backscattered flux: Fb
Incident solar flux: Fsun
- AB is omnidirectional, Ap is unidirectional
- AB is frequency averaged, Ap refers to aphotometric passband
- AB is theoretical, Ap is observational
Ap Fb /Fsun
AB Ap q
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The Lambert Disk
Non-absorbing isotropicscatterer with f() = cos
Same surface brightnessfrom all directions (
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Geometric Albedos, Phase Integrals
Object Ap q
Mercury
Venus
Earth
Moon
Mars
JupiterSaturn
Uranus
Neptune
0.136
0.65
0.367
0.152
0.15
0.520.47
0.51
0.41
0.46
1.0
1.07
0.45
1.07
1.41.3
1.4
1.4
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Observed Magnitudes
If S is the solar flux at the Earth in a certainpassband, the flux leaving an object towardthe Earth is:
If R is the radius of the object, the fluxobserved at the Earth is:
In magnitude units:
where and
F SrAU2 Ap f()
Fobs RAU2 Ap f() SrAU
2AU
2
m mo 5lg rAU 5lgAU m()m() 2.5lg f() mo msun 2.5lg RAU
2 Ap
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Colours
The magnitudes mare usually measured withdifferent broadband filters (U, B, V, R, etc.)
The differences, e.g. BV, are called colour indices
From the magnitude formula for a Solar System
object, we get:
Thus the measured colour index depends on: the solar colour (BV)
the albedo ratio Ap(B)/Ap(V) (true colour)
the phase reddening B()V()
BV (BV)sun 2.5lg Ap(B) /Ap(V) B V
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Phase Curves
At small , a linearformula is often used asphase curve:
Opposition effect: spikein brightness at very small for atmospherelessobjects
PhotometryR2Ap : Size-albedo ambiguity
m()
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Opposition Effect in Saturns A Ring
Cassini image
Cause of thebrightness spike at
opposition:
- Lack of shadowing
- Coherent backscatter
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Light scattering from grains (1)
Examples: the zodiacal light,dust tails in comets, etc.
Observed brightness: collectiveamount of scattered sunlightfrom all grains along the line ofsight
The grain size distributionis
important for interpreting theobservations:
- for grains of radius a, thesurface/volume ratio is a-1
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Light scattering from grains (2)
Large grains or bouldersscatter light like planets
without atmospheres:backscattering
Very small grains (~)
are much more forwardscattering
Jupiters rings seen
against the Sun
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Temperature & radiometry (1)
Incident energy flux (insolation)depends on the distance to theSun and the solar elevation angle
Insolation = Scattering + Thermal
radiation + Heat conduction
The scattering efficiency ismeasured by AB
Thermal emissivityIR:
- Is IR = 1-AB? No, IR0.9 isassumed in general
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Planetary spectra
Common planetaryminerals have spectralfeatures in the IR:
- e.g. stretching of bondswithin molecules
- local variation ofemissivity
Important for chemicalanalysis and thermalmodelling
Infrared spectrum of Mercury
Jupiters spectrum
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Temperature & radiometry (2)
Emitted flux of thermal radiation from theStefan-Boltzmann radiation law:
Assume isothermal, spherical object!
Absorbed insolation per unit time:
Emitted radiation per unit time:
Equilibrium temperature for thermal balance:
FT4
Ein R2 (1 AB )SrAU
2
Eout 4R2
T4
Teq S(1 AB )
4IRrAU2
1/ 4
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Bond albedos & Eq. temperatures
Object AB Teq (K)
Mercury
Venus
EarthMoon
Mars
JupiterSaturn
Uranus
Neptune
0.063
0.65
0.390.068
0.16
0.730.61
0.71
0.57
450
260
250280
220
9073
48
42
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Radar observations (1)
Send a radio pulse toward the object; receiveand analyze the echo
Two main variables: Delay and Doppler shift
Received intensity: I(t,) Find a model of the objects size, shape and
spin that represents I(t,)
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Radar observations (2)
Echo frequency range:
Noise level for integrationtime t:
Received signal:
Signal/Noise ratio:
Toutatis, small near-Earthasteroid
Kleopatra, large main-beltasteroid
D /P
N t D /P 1/ 2
So4D2A2tt
SNRo4D3 / 2A2tP
1/ 2t1/2